In recent memory hard disk drives, high storage capacity and miniaturization are in demand. In order to increase the recording density, it is desired to lower the flying height of a magnetic head and to reduce the unit recording area. Along with this trend, even in a manufacturing step for a substrate for a magnetic disk, the surface qualities of the substrate required after polishing have been severely assessed every year. In other words, in order to satisfy the lowering of the flying height of the magnetic head, surface roughness and microwaviness are required to be reduced. In order to meet such requirements, a polishing slurry capable of reducing scratches of a polished substrate is known (JP2000-15560 A and JP2000-458 A).
Moreover, recently, from the viewpoint of satisfying improvement in surface qualities such as an even higher smoothness and more reduced scratches, and increase in productivity, a multi-step polishing method including two or more steps of polishing steps has been employed (JP2005-63530 A). In a final polishing step of the multi-step polishing method, i.e. a finish-polishing step, in order to meet the requirements of reduction of surface roughness and reduction of scratches, polishing can be carried out with a polishing composition for finishing in which colloidal silica particles are used. On the other hand, in a polishing step prior to the finish-polishing step (rough-polishing step), abrasive grains having relatively larger particle sizes that are capable of realizing a high and practical polishing rate, for example aluminum oxide particles and the like are more likely to be used, from the viewpoint of productivity.